A multigrid algorithm for steady transonic potential flows around aerofoils using Newton iteration
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Abstract
The application of multigrid relaxation to transonic potential-flow calculation was investigated. Fully conservative potential flows around aerofoils were taken as test problems. The solution algorithm was based on Newton iteration. In each Newton iteration step, multigrid relaxation was used to calculate correction potentials. It was found that the iteration to the circulation has to be kept outside the multigrid algorithm. In order to obtain meaningful norms of residuals (to be used in termination tests of loops), difference formulas with asymptotic scaling were introduced. Nonlinear instability problems were solved by upwind differencing using mass-flux-vector splitting instead of artificial viscosity or artificial density. It was also found that the multigrid method cannot efficiently update shock positions due to the (mainly) linear character of individual multigrid relaxation cycles. For subsonic flows, the algorithm is quite efficient. For transonic flows, the algorithm was found robust; its efficiency should be increased by improving the iteration on the shock positions; this is a highly nonlinear process.